Answer:
1.27, -6.27 to the nearest hundredth,
or if you require it in exact form,
-2.5 + √14.25, -2.5 - √14.25.
Step-by-step explanation:
x^2 = -5x + 8
x^2 + 5x = 8
Competing the square:
(x + 2.5)^2 - 6.25 = 8
(x + 2.5) = 14.25
x + 2.5 = +/-√14.25
x = -2.5 + √14.25, -2.5 - √14.25
x = -2.5 + 3.77, -2.5 - 3.77
= 1.27, -6.27.
CAN ANYONE HELP ME WITH THIS
The line in the middle has a right angle, so the angle just above the Y would be 90 degrees.
The angle to the right of y is given as 48.
The three inside angles of a triangle need to equal 180.
So y = 180 - 90 - 48 = 42 degrees.
Which value of m satisfies the inequality 170 − 7m > 99?
Answer:
[tex]\large\boxed{m<\dfrac{71}{7}\to\left\{m\ |\ m<\dfrac{71}{7}\right\}\to m\in\left(-\infty,\ \dfrac{71}{7}\right)}[/tex]
Step-by-step explanation:
[tex]170-7m>99\qquad\text{subtract 170 from both sides}\\\\-7m>-71\qquad\text{change the signs}\\\\7m<71\qquad\text{divide both sides by 71}\\\\m<\dfrac{71}{7}[/tex]
10 because if you minus 170 from 10 it would still be less than 99
An investment fund starts at $0 and grows at a rate of $100 per month. Another fund starts at $4000 and reduces by $720 per year. After how long will the funds have the same amount of money?
Answer: 2 years 1 month
Step-by-step explanation:
2 years 1 month at $100 a month = $2,500
$720 x 2 years = $1,440
$720 / 12 months = $60
$1,440 + $60 = $1,500
$4,000 - $1,500 = $2,500
The two investment funds will have the same amount of money after 25 months. This conclusion is reached by setting up and solving an equation where the monthly growth of the first fund, $100x, equals the monthly decrease of the second fund, $4000 - $60x.
Explanation:Let's denote the time in months that it takes for both investment funds to have the same amount of money as x. The equation that represents the first fund's growth is 100x, as it grows at $100 per month. The equation for the second fund is 4000 - 60x, as it decreases by $720 per year, or $60 per month.
We can set these two equations equal to each other to solve for x: 100x = 4000 - 60x. Solving this equation involves adding 60x to both sides to yield 160x = 4000, and then dividing by 160 to get x = 25. Therefore, after 25 months, both funds will have the same amount of money.
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Which of the following is a description of the data with a correlation coefficient of 0.8?
no correlation
perfect positive correlation
high positive correlation
perfect negative correlation
Answer:
High positive correlation
Step-by-step explanation:
Perfect correlation is 1 or -1(0 is no correlation), the correlation coefficient is .8
It is positive because it is a positive number (closest to positive 1).
This value is close to 1 so it's a high positive correlation.
Answer:
Answer Is C.
Step-by-step explanation:
The vertex of the parabola is at (-2,-3) which of the following could be its equation
A. 2
B.-8
C.8
D.-2
Answer might be d I think
Answer: D -2
Step-by-step explanation:
Questões matemáticas
4) 3a- 4b ( 4 - 7a + 2b ) + b
6) 3mn ( m² + n² - m + 4n - 5 )
8) ( x + √5 )²
9) ( 4x + 2y )²
10) (2w-1,6)²
13) (x+11)(x+18)
15) (x+4,7)(x+3,25)
Considere x=-4, y=48 e z=2,7
17) 2x-y+3z
18) xz+1,57
20) x³+2x²-4x
subtract and simplify
Answer:
D
Step-by-step explanation:
Since the denominators of both fractions are common, then subtract the numerators leaving the common denominator, that is
[tex]\frac{4a+1-2a-7}{a^2-4}[/tex] = [tex]\frac{2a-6}{a^2-4}[/tex]
Answer:
[tex]\boxed{\bold{\frac{2a-6}{a^2-4}}}[/tex]
Explanation:
Apply Rule [tex]\bold{\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}}[/tex]
= [tex]\bold{\frac{4a+1-\left(2a+7\right)}{a^2-4}}[/tex]
Expand [tex]\bold{4a+1-\left(2a+7\right): \ 2a-6}[/tex]
= [tex]\bold{\frac{2a-6}{a^2-4}}[/tex]
Mordancy.
6 points can someone help me
Answer: 39$
Step-by-step explanation: calls=x x=30 30*.05= 1.50 40.50-1.50= 39$
Answer:38.55
Step-by-step explanation:
because you would make x=to 30 for the time and that would make the problem
40.05-0.05*30
0.05*30=1.5 so
40.05-1.5=38.55
If a 30% discount is put on an item, and the sale price is $206.50, then what was the original price?
Answer:
295
Step-by-step explanation:
.3 x 295 = 88.5
295 - 88.5 = 206.5
In the diagram, which angle is part of a linear pair and part of a vertical pair?
BFC
CFG
GFD
EFA
Answer:
∠EFA
Step-by-step explanation:
Linear pair : A linear pair is a pair of adjacent angles formed when two lines intersect and the sum of these angles is 180°
Vertical angles: The opposite angles formed by the two intersecting lines are called vertical angles.
Option 1) ∠BFC
Line BE and CF intersect at point F
So, the two adjacent angles formed when two lines intersect are ∠BFC and ∠EFC.
These are linear pair.
So, ∠BFC is a part of linear pair.
Now by the definition of vertical angles , ∠BFC has no vertical pair.
So, ∠BFC is not a part of vertical pair.
Option 2) ∠CFG
According to the definition of linear pair ∠CFG is not a part of linear pair.
According to the definition of vertical pair ∠CFG is not a part of vertical pair.
Option 3) ∠GFD
According to the definition of linear pair ∠GFD has a linear pair ∠AFG
Thus ∠GFD is a part of linear pair
According to the definition of vertical pair ∠GFD is not a part of vertical pair.
Option 4) ∠EFA
According to the definition of linear pair ∠EFA has a linear pair ∠EFD
Thus ∠EFA is a part of linear pair
According to the definition of vertical pair ∠EFA has a ∠BFD vertical pair.
Thus ∠EFA is a part of vertical pair.
Hence ∠EFA is part of a linear pair and part of a vertical pair.
Answer:
D) EFA
Step-by-step explanation:
Let's see the definition of linear pair and vertical angles.
A linear pair of angles are the adjacent angles, when the angles add upto 180°.
Vertical angles are the opposite angles when the two lines are intersecting. The vertical angles are equal in measure.
In the given figure there are only two lines, they are AD and BE. Othere are just rays.
By look at the figure, ∠EFA is a linear pair to∠EFD and as well as vertical angle to ∠DFB.
Therefore, the answer is D) EFA
The cost in dollars, y, of a large pizza with x toppings from Pat’s Pizzeria can be modeled by a linear function. A large pizza with no toppings costs $14.00. A large pizza with 2 toppings costs $17.50.
What is the cost of a pizza with 5 toppings? Round to the nearest penny.
$22.75
Start by finding the cost of each topping. Subtract $17.50 minus $14.00 to find that adding 2 toppings costs $3.50. Now, divide $3.50 by 2 to find that the cost for adding only one topping is $1.75.
Then, multiply $1.75 by 5 to find how much it costs to add 5 toppings. You get $8.75.
Finally, add the cost of 5 toppings to the cost of a large pizza with no toppings. $14.00 plus $8.75 equals $22.75, so a large pizza with 5 toppings costs $22.75.
Answer: $22.75
Step-by-step explanation:
Given : The cost in dollars, y, of a large pizza with x toppings from Pat’s Pizzeria can be modeled by a linear function.
A linear function is given by :-
[tex]y=mx+c[/tex] (1)
, where m is slope (rate of change of y w.r.t x) and c is the y-intercept.
A large pizza with no toppings costs $14.00.
i.e. for x=0 , y= 14
Put theses values in (1) , we get
[tex]14=m(0)+c\\\Rightarrow\ c=14[/tex] (2)
A large pizza with 2 toppings costs $17.50.
i.e. for x=2 , y= 17.50
Put theses values in (1) , we get
[tex]17.50=m(2)+c[/tex]
Put value of c from (2)
[tex]17.50=2m+14\\\\[/tex]
Subtract 14 from both sides , we get
[tex]3.50=2m[/tex]
Divide both sides by 2 , we get
[tex]1.75=m[/tex]
Put m= 1.75 and c= 14 in (1) , the linear function representing cost of large pizza becomes [tex]y=1.75x+14[/tex]
At x= 5
[tex]y=1.75(5)+14=8.75+14=22.75[/tex]
Thus , the cost of a pizza with 5 toppings= $22.75
Plz answer quick dont have much time left on the it’s asking what the surface area is
Answer:
Surface Area = Sum of area of all sides = 203.2 Units Squared
Step-by-step explanation:
Top and Bottom: A = ((.5*4*6) + (.5*3.6*2)) * 2 => (12+3.6) *2 => 15.6*2 = 31.2
Sides: A = ((5*10)+(3.6*10)) *2 => (50 + 36) *2 => 86*2 = 172
Total Surface Area = Top + Bottom + Sides = 203.2 units squared
if 1/4
inch equals 50 miles, find the miles represented by 4 1/2
inches.
Answer:
900 miles
Step-by-step explanation:
Well, 200 miles is 1 inch. 100 miles is 1/2 an inch.
Answer:
900
Step-by-step explanation:
Given: 1/4 in. = 50 miles
Find the amount of miles per inch. Multiply 4 to both sides of the equation.
(1/4 in.) x (4) = (50 miles) x (4)
4/4 in. = 200 miles
1 in. = 200 miles
Now, find the amount of miles for 4 1/2 in. Multiply 4 1/2 to both sides.
Note that 4 1/2 = 4.5
(1 in.)(4.5) = (200 miles) x (4.5)
4.5 = 200 x 4.5
4.5 = 900
900 miles is your answer.
~
Choose the point-slope form of the equation below that represents the line that passes through the points (-6, 4) and (2.0).
y-4 =-1/2(x+6)
y - 4 = 2(x + 6)
y+6=-1/2(x-4)
y+ 6 = 2(x-4)
Answer:
y - 4 = -1/2(x+6).
Step-by-step explanation:
The equation of the line is: y - y0 = m(x-x0)
If the line passes through the points (x1, y1)=(-6, 4) and (x1, y1)=(2, 0). Then, the slope is:
[tex]m = \frac{y1-y0}{x1-x0} = \frac{0-4}{2-(-6)} = -\frac{1}{2} [/tex]
Then, the equation is: y - 4 = -1/2(x+6).
if you flip a fair coin 5 times, and see 3 heads and 2 tails, what fraction of the time will you expect to see a head on the sixth flip
A:1/64
B:1/2
C:3/5
D:2/3
E:5/6
I hope I'm not wrong here, but B.1/2? Only because its a 50% chance
The fraction of the time will you expect to see a head on the sixth flip will be 1/2.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Here the sample variables are = [3 heads , 2 tails]
The number of the times coin flipped = 6 times
Probability of the flipping the coin and having head will be
P(A)=3/6=1/2
Hence the fraction of the time will you expect to see a head on the sixth flip will be 1/2.
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90%
What are the exact solutions of x2 – 5x - 1 = 0? (5 points)
x=51 V29
x =
80%
5+29
x = 51 V21
20%
x = -51 V21
For this case we must find the solutions of the following quadratic equation:
[tex]x ^ 2-5x-1 = 0[/tex]
We solve by means of[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
Where:
[tex]a = 1\\b = -5\\c = -1[/tex]
Substituting:
[tex]x = \frac {- (- 5) \pm \sqrt {(- 5) ^ 2-4 (1) (- 1)}} {2 (1)}\\x = \frac {5 \pm \sqrt {25 + 4}} {2}\\x = \frac {5\pm\sqrt {29}} {2}[/tex]
Finally, the roots are:
[tex]x_ {1} = \frac {5+ \sqrt {29}} {2}\\x_ {2} = \frac {5- \sqrt {29}} {2}[/tex]
Answer:
[tex]x_ {1} = \frac {5+ \sqrt {29}} {2}\\x_ {2} = \frac {5- \sqrt {29}} {2}[/tex]
The price of a cd was decreased by 20% to £7.68. What was the price before the decrease?
Answer:
£9.6
Step-by-step explanation:
x = the original price of a CD
£x = 100% of the original price
The price of a CD was decreased by 20% to £7.68.
This means:
£7.68 = 100% - 20%
£7.68 = 80% of the original price
From this, we will find 1% of the original price.
£7.68 ÷ 80 = 1%
£0.096 = 1%
Since the original price ( x ) = 100% of the original price, we will find 100% of the original price.
£0.096 × 100 = 100%
£9.6 = 100%
Therefore, the original price of a CD = £9.6
The price before the decrease was approximately £9.60.
Explanation:To find the price before the decrease, we need to calculate the original price before the 20% decrease. Let's call the original price 'x'. We know that after the 20% decrease, the price is £7.68.
So, if we take 20% of 'x' and subtract it from 'x', we should get £7.68. Mathematically, this can be expressed as:
x - 0.20x = 7.68
Simplifying the equation, we have:
0.80x = 7.68
Dividing both sides of the equation by 0.80, we find that 'x' is approximately 9.60. Therefore, the price before the decrease was approximately £9.60.
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Draw a right triangle with 5 cm and 7 cm perpendicular sides. Find its perimeter.
Answer:
20.6 (3sf)
Step-by-step explanation:
a^2 + b^2 = c^2
5^2 + 7^2 = 74
c= root 74
5 + 7 + root 74 = 12 + root 74 = 20.6 (3sf)
Need Help:> :> ^^^^^^^^^
Multiply the numbers by 2
7*2=14
14*2= 28
28*2=56
Answer is 56
ANSWER
56
EXPLANATION
We want to find the next number in the sequence,
7,14,28,
Observe that, there is a common ratio of 2 among the terms.
That is ,
7(2)=14
14(2)=28
Therefore the next term is
28(2)=56
Therefore the number that goes into the box is 56.
Mr. Lee asks a student to solve the following system of linear equations. {-28=-40q-14p 10q+4=2p Which ordered pair (p, q) is a solution to the system? (-7/5,-2) (-2,-7/5) (0, 2) (2, 0)
Answer:
p = 2 , q = 0
Step-by-step explanation:
Solve the following system:
{-28 = -14 p - 40 q | (equation 1)
10 q + 4 = 2 p | (equation 2)
Express the system in standard form:
{14 p + 40 q = 28 | (equation 1)
-(2 p) + 10 q = -4 | (equation 2)
Add 1/7 × (equation 1) to equation 2:
{14 p + 40 q = 28 | (equation 1)
0 p+(110 q)/7 = 0 | (equation 2)
Divide equation 1 by 2:
{7 p + 20 q = 14 | (equation 1)
0 p+(110 q)/7 = 0 | (equation 2)
Multiply equation 2 by 7/110:
{7 p + 20 q = 14 | (equation 1)
0 p+q = 0 | (equation 2)
Subtract 20 × (equation 2) from equation 1:
{7 p+0 q = 14 | (equation 1)
0 p+q = 0 | (equation 2)
Divide equation 1 by 7:
{p+0 q = 2 | (equation 1)
0 p+q = 0 | (equation 2)
Collect results:
Answer: {p = 2 , q = 0
Answer:
p = 2 , q = 0
Step-by-step explanation:
Trust me
use the associative property of addition to find the total of 1,10, and 18 in two different ways.
Answer:
(1+10)+18=11+18=29; 1+(10+18)=1+28=29
Step-by-step explanation:
the associative property of addition means that no matter in what order you group the numbers for addition the results come out to be the same.
using the associative property of addition to find the total of 1,10, and 18 in two different ways
first: (1+10)+18
=11+18
=29
second: 1+(10+18)
=1+28
=29!
The solution to x2 – 10x = 24 is
Answer:
x = - 2, x = 12
Step-by-step explanation:
Given
x² - 10 x = 24 ( subtract 24 from both sides )
x² - 10x - 24 = 0 ← in standard form
To factorise the quadratic
Consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (- 10)
The factors are - 12 and + 2, since
- 12 × 2 = - 24 and - 12 + 2 = - 10, thus
(x - 12)(x + 2) = 0
Equate each factor to zero and solve for x
x - 12 = 0 ⇒ x = 12
x + 2 = 0 ⇒ x = - 2
The solution of this quadratic equation to x² – 10 x = 24 is x = - 2 & x = 12
What is a quadratic equation?A quadratic is a sort of problem that deals with a variable accelerated by using an operation called squaring. This language derives from the area of a rectangular being its facet period expanded with the aid of itself. The phrase "quadratic" comes from quadrant, the Latin word for square.
x² – 10 x = 24
⇒ x² +2X -12X -24 = 0
⇒ x (x - 2) -12(x - 2) =0
⇒ x = 12 OR ( x = -2)
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What the equation for a slope of 3 and y-intercept of (0,-2)
The answer is y = 3x - 2
Y=3x-2
The formula y=mx+b is the slope intercept formula. You would enter the information of the problem into the equation.
You would place the slope in the place of m and the y intercept in the place of b.
Since it is a negative slope it would be -2 instead of +2 if it was positive.
Please help with geometry! 30 points
Step-by-step explanation:
*****************here is the answer
area=28.61+12=40.61**************
1. What is the value of x in the figure?
2. What is the value of y in the figure?
3. What is the value of z in the figure?
Answer:
[tex]x=6\sqrt{5}\\ \\y=3\sqrt{5}\\ \\z=6[/tex]
Step-by-step explanation:
The height of the right triangle drawn to the hypotenuse is geometric mean of two segments of hypotenuse, so
[tex]z^2=12\cdot 3\\ \\z^2=36\\ \\z=6[/tex]
By the Pythagorean theorem,
[tex]x^2=12^2+z^2\\ \\x^2=144+6^2\\ \\x^2=144+36\\ \\x^2=180\\ \\x=6\sqrt{5}[/tex]
and
[tex]y^2=z^2+3^2\\ \\y^2=6^2+9\\ \\y^2=36+9\\ \\y^2=45\\ \\y=3\sqrt{5}[/tex]
Kylie needs to pack her baton for a color-guard competition. The baton is 38 inches long. Will it fit in a rectangular box with a base of 13 inches by 35 inches and a height of 13 inches?
What is the diagonal??
HELP ASAP
Quiz is tmmr
Answer:
The diagonal is 39.54 in
Step-by-step explanation:
First we use the Pythagorean theorem to calculate the length of the diagonal of the base.
If the base measures 13 inches by 35 inches then the diagonal is:
[tex]c = \sqrt{13^2 +35^2}\\\\c= 37.34\ in[/tex]
Now we use the Pythagorean theorem again to find the diagonal of the cube.
If the height of the box is 13 inches and the diagonal of the base is 37.34 inches then the diagonal of the cube will be
[tex]z = \sqrt{37.34^2 +13^2}\\\\z= 39.54\ in[/tex]
The baton will fit in the box if it is placed in the direction of the diagonal of the cube, since:
39.54\ in > 38 inches
Using the 3D Pythagorean theorem, the diagonal of the box is calculated to be approximately 39.53 inches, which means that Kylie's 38-inch baton will fit inside the box diagonally.
Explanation:Kylie needs to check if her 38-inch long baton will fit diagonally in a box with dimensions of 13 inches by 35 inches by 13 inches. To determine whether the baton will fit, she needs to find the length of the longest diagonal of the box. This is solved by using the 3D Pythagorean theorem, which is an extension of the traditional Pythagorean theorem applied to three dimensions.
To find the length of the diagonal (d), we use the formula:
d = √(l² + w² + h²)
Where l is the length, w is the width, and h is the height of the box. Substituting the given values:
d = √(13² + 35² + 13²)
d = √(169 + 1225 + 169)
d = √1563
d ≈ 39.53 inches
The calculated diagonal length of approximately 39.53 inches indicates that Kylie's baton, which measures 38 inches, will indeed fit inside the box diagonally.
a number c increased by 17
c increased by 17
Increased = +
c + 17 is the answer
Answer:
Error question or wrong
Margaret has a bag containing 6 red
chips and 6 blue chips. What is the
probability of drawing two red chips in two
draws without replacement?
Answer:It will be 2/12
Step-by-step explanation:
6 blue chips 6 red chips
6+6=12 so 2 red chips to 12 =2/12
Which expression is equivalent to 64y^18-1000z^6?
The expression (4y^6)^3 - (10z^2)^3 is equivalent to 64y^18 - 1000z^6.
Explanation:Factor out common powers:
64y^18 = (2^6)(y^3)^6
1000z^6 = (10^3)(z^2)^3
Rewrite the expression with factored terms:
64y^18 - 1000z^6 = (2^6)(y^3)^6 - (10^3)(z^2)^3
Apply power of a power rule:
(a^m)^n = a^(mn)
(2^6)(y^3)^6 = 2^(66) * y^(36) = 2^36 * y^18
(10^3)(z^2)^3 = 10^(33) * z^(2*3) = 10^9 * z^6
Substitute back the simplified terms:
2^36 * y^18 - 10^9 * z^6 = (4y^6)^3 - (10z^2)^3
Therefore, (4y^6)^3 - (10z^2)^3 is the equivalent expression to 64y^18 - 1000z^6. Both expressions involve the difference of cubes of binomials, with one focusing on powers of 4y^6 and the other emphasizing powers of 10z^2.
Identify the asymptotes of y = 3/x +2.
Answer:Vertical Asymptotes: x=0
Horizontal Asymptotes: y=2
Here’s a graph picture...